The only problem is to develop a series of simple commands to do
this task.

Here's my set of simple commands:
git checkout master
git pull origin master
git apply my_patch_file_name_goes_here
git checkout staging
git pull origin staging
git cherry-pick master
git push origin staging
These commands will work, unless some patch already applied to staging has
messed with the files in such a way that the cherry-pick fails. When the
cherry-pick fails, I don't know of a way to do it without thinking. At
that point, thought will be necessary. Most often I will finish the
cherry-pick by doing
git mergetool
And solving the merge conflicts that show up, then committing the results
using the command that git gave me in the error message that said the
cherry-pick wouldn't apply.
Thanks,
Carl

Here's Carl's simple amended recipe, with my changes/comments. Can those
that understand confirm this is OK?

git checkout master # changes us to a local branch called master

git pull origin master # updates our local master branch from the source
branch called origin
git apply my_patch_file_name_goes_here # applies a downloaded patch. An
alternative would be to edit the local files at this point
git commit -a # commits the changes made by applying the patch/editing the
files

git checkout staging # swap to local branch called staging

git pull origin staging # updates the local staging branch from the source
branch called origin
git cherry-pick master # I assume this updates my local staging branch with
the new commit in my local master branch
git push origin staging # This appears to push my local staging branch to
the remote origin - not what we want?

I'm waving in the dark a bit here, but I am Graham's idiot and I want to
change one line in the CG. Will this work:

git pull # updates my master branch, which is the only one I have, from
remote

# edit my file
git commit -a

git push staging # I believe this pushes any commits I have to the remote
branch called staging